In a Certain Discrete Math Class, Three Quizzes Were Given $\# 1$

question 8

Essay

In a certain discrete math class, three quizzes were given. Out of the 30 students in the class: 15 scored 12 or above on quiz #1,
12 scored 12 or above on quiz #2,
18 scored 12 or above on quiz #3,
7 scored 12 or above on quizzes $\# 1$ and $\# 2$ ,
11 scored 12 or above on quizzes $\# 1$ and $\# 3$ ,
8 scored 12 or above on quizzes #2 and #3,
4 scored 12 or above on quizzes $\# 1$ , #2, and #3.
(a) How many scored 12 or above on at least one quiz?
(b) How many scored 12 or above on quizzes 1 and 2 but not 3?

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Definitions:

Upper Paleolithic

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The process by which a group or individual modifies their customs and behaviors to fit into a new cultural environment.

Prominent Cheekbones

A facial feature where the cheekbones are more pronounced or high on the face, often considered an aesthetic or characteristic trait in various cultures.

Higher Foreheads

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